The coefficients $a, b, c$ in the quadratic equation $a x^2+b x+c=0$ are from the set $\{1,2,3,4,5,6\}$. If the probability of this equation having one real root bigger than the other is $p$, then 216 p equals :

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{D}>0 \ & \mathrm{~b}^2>4 \mathrm{ac} \ & \mathrm{b}=3:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1) \ & \mathrm{b}=4:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1)(1,3)(3,1) \ & \mathrm{b}=5:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1)(1,3)(3,1)(1,4)(4,1) \ &(1,5)(5,1)(1,6)(6,1)(2,3)(3,2)(2,2) \ & \mathrm{b}=6:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1)(1,3)(3,1)(1,4)(4,1) \ &(1,5)(5,1)(1,6)(6,1)(2,3)(3,2)(2,4)(4,2)(2,2) \end{aligned}$ fav. cases $=38$ Prob. : $\frac{38}{6 	imes 6 	imes 6}$

The coefficients $a, b, c$ in the quadratic equation $a x^2+b x+c=0$ are from the set $\{1,2,3,4,5,6\}$. If…

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